Surmise relations between tests—mathematical considerations Original Research Article

In 1985, Doignon and Falmagne introduced surmise relations for representing prerequisite relationships between items within a body of information for the assessment of knowledge. Often it is useful to partition such a body of information into sub-collections. As we are primarily interested in psychological applications, we refer to these sub-collections as tests. We extend the concept of surmise relations between items within tests to surmise relations between tests. Three different kinds of surmise relations between tests are investigated with respect to their properties. Furthermore, the corresponding knowledge spaces for tests and their bases are introduced. The relationship of this set theoretical approach to a Boolean matrix representation is discussed. Finally, we give a short overview about the further research regarding this mathematical model. It will be the foundation for a software system that will be used for analyzing test data. Other applications in fields like curriculum development and structuring hyper-texts can easily be imagined.